Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [permutations]

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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permutation with limited repetition

Suppose there are 8 boxes and many balls of 7 different colours. We have to fill all the boxes with balls with the restriction that balls of a particular colour can not be placed in more than 2 boxes. It may be possible that ball of a particular…
user1463308
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Regular abelian groups of order $2^m$ and type $(2,2,\ldots,2)$

I was wondering if there is a systematic way to construct the regular Abelian groups of order $2^m$ and type $(2,2,\ldots,2)$. Since the permutation group needs to be regular, it should act transitively on a set of size $2^m$. For example, if…
AG.
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For permutation $\sigma$ let $\sigma T(X_1, \ldots, X_n) = T(X_{\sigma(1)},\ldots, X_{\sigma(n)})$, why then $\tau(\sigma T) = (\tau\sigma) T$?

I've encountered this first in Lang's Algebra (believe me, I've mastered major parts of that book), but the first notation is actually from Lee (Introduction to Smooth Manifolds, Chapter 11. Tensors) where $T$ is a covariant tensor and the goal is…
toxic
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calculating variations/permutations

I wonder if someone could give me the formula - or better still the answer to this. I want to figure out how many different configurations I could get from 2 colors or symbols (Red/Black)varranged in sequences of five. repeating colors is ok. So for…
Lesley
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Possible Tetris Field Permutations

The game of Tetris is played on a grid of squares that is 10 squares across and 20 squares high. Over the course of the game, tetrominoes (geometric shapes consisting of four squares connected orthogonally) fall from above and lock into place…
JTstudent
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Combination or Permutation?

I read this puzzle as below. You have 40 boxes, all placed in a row at exact intervals of 1 meter. You also have 9 balls(all same type). You wish to place all the balls in the boxes, no more than one ball in each box, so that there are…
goldenmean
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Determine how many $4$ digit numbers divisible by $5$ can be generated using the set: $\{1,3,5,6,7,8\}$

Determine how many $4$ digit numbers divisible by $5$ can be generated using the set: $\{1,3,5,6,7,8\}$. Repetion is not allowed. If I am not wrong, we have to use permutation in this question right? I still do not understand how to solve this…
Muhammad Khan
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Working Out Combinations For 9 Pegs Of 9 Possible Colours ( Mastermind Game )

I have written a Mastermind clone where there are 9 peg-slots where each of the peg-slots can be 1 of 9 colours. I cannot seem to get my head round working out the number of permutations for particular repeated counts of any colours :( I am wanting…
Alex Ainsworth
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Count of permutations with N fixed order elements (chromozomes)

I found this question It is about count of permutations with preserving order of elements in different sets, eg. in case of two sets [A,B,C] [1,2,3] one of solutions might be {A 1 B C 2 3}. In my case there is unlimited number N of sets of variable…
wtdmn
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Number of permutations such that no two adjacent elements in the original remain adjacent

$N$ students are standing in a line. How many permutations exist such that no two students who were originally next to each other remain next to each other? Suppose $n=4$ and assuming the original permutation to be $ABCD$,then valid permutations…
SHB
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The students $S_1, S_2,...S_{10}$ are divided into 3 groups A, B and C

It can be seen as distributing n unique objects above m groups The students $S_1, S_2,...S_{10}$ are divided into 3 groups A, B and C such that each group has at least one students and C has at most 3. Find possibilities of forming…
Aditya
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formula of pascal's triangle

I want to make a program for pascal's triangle,I was reading through the details and found something like this: 0: 1 1: 1 1 2: 1 2 1 3: …
Aayman Khalid
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Calculating permutations if the sequences have to be in ascending order?

How would you go about calculating the number of permutations in ascending order. Obviously if you had (a set of) 3 numbers you have $ 3! $ permutations: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1) But only one of these is in ascending…
Jake Burton
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Number of ways to color sides of square with rotation

The edges of a square are to be colored either red, blue, yellow, pink, or black. Each side of the square may only have one color, but a color may color many sides. How many different ways are there to color the square if two ways that can obtained…
SolvingTrainee
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Help me out on permutation and combination

I have to get all combinations of a six digit number where each digit is unique. Its clear that this combination will not have a 0 at the start as it will not be a valid six digit number. Help me on how to attack this problem.
bragboy
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